Artificial transformer



Feb. 2, 1960 J..| FL-.ANAGAN 2,923,784

ARTIFICIAL TRANSFORMER J. L. FLANAGAN ATTORNEY Feb. 2, 1960 J. L. FLANAGAN 2,923,784

ARTIFICIAL TRANSFORMER Filed Dec. 50, 1957 2 Sheeos-Slfxeel 2 J .FLANAGAN BY HWQNJ ARTIFICIAL l TRANSFORMER James L. Flanagan, New Providence, NJ., assigner to yBell Telephone Laboratories, Incorporated, New York, N.Y., a corporation of New York Application December 30, 1957, Serial No. 705,998

15 Claims. (Cl. S30-85) This invention relates generally to the coupling of a source of electric signals -to a load and tothe continuous maintenance of prescribed conditions of impedance match between them despite variations of the self impedance of either one.

In an ideal close-coupled transformer, the ratio of primary to secondary voltage is directly proportional to the ratio (N: l) of the number of turns in the primary winding to the number in the secondary winding. Similarly, the ratio of primary to secondary current is inversely proportional to the turns-ratio, (N :1). The impedance presented at the primary terminals of the transformer is equal to the impedance of the secondary circuit multiplied bythe square of the turns-ratio (N2). Uses of such transformers are manifold.

./ariabley transformers wherein the effective turns-ratio is altered in discrete steps bysliding contacts are well known; however, such transformers typically are usable only over a restricted range of frequencies and are characterized by noise generated as the tap is moved discontinuously from turn to turn. Moreover, servo-mechanisms to effect dynamic variations of the position of the movable tap are complex and cumbersome. A transformer designed for use at very low frequencies requires a bulky and heaw iron core to obtain the necessary selfinductance to permit linear operation at such low frequencies. For many laboratory uses such an iron core transformer is prohibitively expensive, and an unacceptable time delay in development work may attend the fabrication of such special units.

. It is an object of this invention to provide a compact, lightweight unit which will simulate in external characteristics an ideal transformer with continuously variable turns-ratio, which can be adapted to operate over a range of frequencies from the very lowest frequencies to the megacycle range.

Another object of this invention is to provide an artilicial transformer by which the apparent impedance of a passive network may be altered without destroying its desired frequency response characteristics.

Another object of this invention is to provide an artilicial transformer with a control by which the varying impedance of a load may be continuously matched to that of a generator.

, Another object of this invention is to provide a device that will transform the sign as well as the magnitude of a passive impedance (for example, a positive resistance can be made to appear as a negative resistance of arbitrary magnitude, or an inductive reactancecan be made to appear as a capacitive reactance of arbitrary magnitude).

To these ends, the invention consists of certain novel connections of a voltage amplifier and a currentamplier; namely, that each` amplifier is connected in a feedback relation to the other to -forrn the functional equivalent `of a magnetic transformer with effective turns-ratio responsive to a controlled variation of the amplifier gains.

The principles governing the fabrication and use of Faternted Feb. 2, 1360 such artificial transformers, together with further objects and advantages thereof, will best be comprehended by reference to the following description of illustrative embodiments thereof, taken rin connection with the accompanyingdrawings, in which:

Fig. 1 is a circuit diagram of an ordinary close-coupled magnetic transformer which transforms a primary voltage el and a primary current il into a secondary voltage e2 and a secondary current i2 in accordance with a turnsratio N: l;

, Fig. 2 is a block diagram of an ideal artificial transformer device constructed in accordance with this. in-

vention; v

Fig. 3 is a more detailed block diagram representative of a practical embodiment of the invention;

Fig. 4 is a partial schematic diagram showing substantially the same circuit shown in Fig. 3 with the elements further broken down and grouped in a functional manner;

Fig. 5 is a schematic diagram representative of a specific embodiment of the invention which has been found to be useful in the laboratory; and

Fig. y6 is a schematic diagram of a simple transmission system incorporating the invention. l

Referring now to the drawings, Fig. 1 represents a conventional close-coupled magnetic transformer having a primary winding Il and a secondary winding 2. Both windings link a common core 3. The turns-ratio, N, of the `number of primary winding turns around the core to the number of secondary turns determines the voltage and current ratios of the transformer.

Externally, the transformer presents four terminals, two input terminals 4 and 5 connected to the primary Winding and two output terminals 6 and 7 connected to the secondary winding. The input current, i1, and-the input voltage, e1, are related to the output current i2 and output voltage e2 through the turns-ratio.

Thus

and

er N (2)l Further, a secondary load impedance, Z2, viewed from the primary is ymultiplied by the square of the turnsratio, i.e. I.; l

and conversely, for a primary impedance Z1, Viewed from the secondary side:

rlhese equations describe an ideal close-coupled transformer. They quite accurately define the performance of a conventional close-coupled iron cored transformer over a band of frequencies. For a well designed transformer these relations can be made to hold for about seven octaves in frequency. Y

Consider now the circuit of Fig. 2. In it an ideal current amplifier 1t), connected to transfer signals from left to right, is interconnected with an ideal voltage amplifier 1l, connected to transfer signals from right to left. The input terminals 12 and 13 of the current amplifier lll are connected in series with the output terminals 14 and l5 of the voltage amplifier 11 and with the input terminals 16 and 17 of the circuit. The output terminals 18 and 19 of the current amplifier ltlandthe input terminals Ztl and 21 of the voltage amplifier 11 are connected in parallel with the output terminals 22 and 23 of the circuit. In other words, the amplifiers are connected together in the specified manner to form a feedback loop. In consequence, the input current i1 of the circuit is equal to the input current of the current amplifier 10, and the input voltage of the amplifier 11 is the output voltage e2 of the device. The ideal current amplifier 10 has a constant ratio Ki of output current i to input current i1, i.e.:

@ I--Kl (3) An ideal current amplifier has a zero input resistance so that its insertion in the circuit does not affect the current to be measured and the output current is dependent 'solely upon the input current. Since, by hypothesis, the output current i0 depends only on input current, i1, it is independent of output voltage, e2, that is,

ez i1=constant vanishes, and its reciprocal, the output impedance eg t'o il=constant is infinite. Accordingly, the ideal current amplifier 10 may be characterized by a Zero input impedance, an infinite output impedance, and a constant gain factor. By itself it is both asymmetrical and unidirectional; a current applied to the output does not generate a current at the input.

Similarly, the ideal voltage amplifier 11 has a constant ratio KE of output voltage e0 to input voltage e2,

Since output voltage e0 depends only on input voltage e2, the output impedance Pn) l e2=constant vanishes. Additionally, since a voltage amplifier preferably should not load the source of input voltage, its input impedance is preferably innite. Accordingly, the ideal voltage amplifier 11 is characterized by an infinite input impedance, a Zero output impedance, and a constant gain factor. It is also asymmetrical and unidirectional. These characteristics of ideal amplifiers must hold whether the gain factors are greater or less than unity. Thus, as used in this specification, and in the appended claims, the input and output terminals of voltage amplifiers and of current amplifiers are designated with respect to impedance levels rather than signal levels. It will be apparent that in Fig. 2 the output current i0 of the current amplifier 10 is the total output current i2 of the device, i.e.:

and the output voltage e0 of the voltage amplifier 11 is equal to the voltage input e1 of the device, i.e.:

Accordingly, the device of Fig. 2 is governed by the following relations:

variable by well known expedients. Four cases are of interest:

Case 1.-If Ke=K1=N=a positive and real constant, then the circuit functions as an ideal, close-coupled :instantaneous pOWel' Out.

Case 2,-If KeKi, but both are positive and real, the general terminal Relations 7, 8 and 9 still hold out:

mstantaneous power 1n e111 K ,ez :fem

and power out may be greater or less than power in,

depending upon the ratio Ke/Ki; the transformer may consume power or act as a source of power.

Case 3.-If Ki and Ke are real, and either (but not both) is negative, then the transformer functions as a negative, impedance converter, transforming a positive load impedance at one set of terminals into a negative impedance at the other pair of terminals; i.e., the transformer changes the sign of a given impedance R R for resistive loads; and (rl-jx) (rjjx) for reactive loads. In thisl case the transformer circuit supplies power to the driving source.

Case zf lf K1 and Ke are complex quantities; i.e., if the amplifiers exhibit phase shift, then and the complex voltages, currents and impedances may be manipulated by adjusting the phase characteristics of the amplifiers. If:

By properly adjusting the phase characteristics of the amplifiers, various effects can be produced. The first three cases are just particular forms of this fourth and general case. For example, a complex load impedance may be made to appear as its complex conjugate at the other terminals if: {Ki} lKe|=1 and (0e-P0)=(203) where 62 is the phase angle of the load impedance, then By this choice of phase characteristics, the sign of the imaginary or reactive term of the load impedance has been changed. A similar choice of phase can be made to change the sign of the real part (or resistive component).

Fig. 3 represents a device having output and input impedances more representative of practical amplifiers, when connected as described for the device of Fig. 2. Here the circuit is driven from a source es with self impedance Z1 connected to the primary side, and a load impedance Z2 is connected across the secondary terminals.

A resistor 38 of value R is connected between input terminals 32 and 33 of the current amplifier y30. Resistor 39 of Value r1 is connected effectively in series with output terminals 34 and 35 of the voltage amplifier 31, and the output resistance 40 of value r2 shunts the output terminals 36 and 37 of the current amplifier 30. Z1 represents the source impedance of the circuit driving the primary with a source voltage es as seen from the input terminals 16 and 17 of the device. Z2 represents a secondary circuit load impedance as seen from the output terminals 22 and 23 of the device. In Fig. 3 (where the circuit is assumed to be driven from the primary side and loaded on the secondary side), the output i of the current amplifier is not exactly identical to secondary current i2, and the output e0 of the voltage amplifier is not exactly equal to the primary voltage e1, but rather:

Wherefore, combining Equations 22 through 25, it follows that the input terminals present an apparent impedance given by:

Z2 z (27) then 2 t2 (2s) 'f2 and lgl, or agria, (29) and since Equation 26 simplifies to:

ge-teamed@ 80) l Further, if I (fri-R) KiKeZz (31) then l el/ilKiKeZg or aKeez (33) Essentially the same conditions apply when the circuit is driven from a source connected to the secondary terminals and a load impedance is connected to the primary terminals. Equations 27 and 31 means that the output impedance (r2) of the current amplifier rnust be high compared to the impedance level of the secondary circuit, and, the sum of the output impedance (11) of the voltage amplifier andthe input impedance (R) of the current amplifier must be low compared with the impedance refiected at the primary terminals. o Both of these conditions can be easily realized to a satisfactory degree in practical circuits, of which Fig. 5 is an example.

Many varieties of amplifiers may be employed in practicing the invention; but stability and the range of useful operation will depend upon the degree to which the amplifiers employed have the characteristics of ideal amplifiers.

Fig. 4 is a Ypartial schematic diagram of an embodiment comprising a voltage amplifier 31 represented as the alternating current equivalent circuit for a triode tube, anda current amplifier 30 represented by a conventional alternating current equivalent circuit S0 for a pentode tube, together with the resistor yR and a phase inverting stage 5S, proportioned to provide a voltage gain -K3. This circuit will be recognized as equivalent to Fig. 2 wherein Ki is replaced by the product R K2 K3 and Ke is replaced by K1. To permit grounded operation of both amplifiers, the points 33 and 34 are grounded. The input to the current amplifier, appearing across the resistor R is, then, in opposite phase to the output of the voltage amplifier. Accordingly, `an additional phase reversal in one of the amplifiers, as indicated by the negative sign of (-Ka), is necessary to correspond to the feedback arrangement'of Figs. 2 and 3. Both the triode and pentode stages of Fig. 4 produce phase inversions of 180 degrees so that the net effect of the circuit is exactly identical to thatof the circuit in Fig. 3.

The device exhibits the characteristics of a transformer with turns-ratio N when the factors are adjusted so that K1=K2K3R=N Variations of K1 and the other factors in a manner to preserve the Relations 34 result in a corresponding variation in equivalent turns-ratio. The control of amplifier gain factors to achieve wide Variations of N may be accomplished by means well known in the art. As a practical matter there is usuallyl no need for N to be less than unity since one may simply reverse the primary and secondary connections.

The maximum value of N that can be achieved is determined largely by stability margins of the circuit as a feedback device. Ns in the range from one to ten have been attained with relatively little attention to the phase characteristics of the circuit.

Fig. 5 is a schematic diagramof an artificial transformer which has been employed to couple passive networks in connection with electrical analog studies of acoustical systems.

The voltage amplifier 31 comprises the pentode V1 in tandem with the cathode follower V2. The current am plifier comprises the two pentode stages V3 and V4 which amplifythe voltage produced across the resistance, R, by the input current. As in the circuit of Fig. 3,. grounded operation of the amplifiers requires that the output of the voltage amplifier and input of thel current amplifier be connected series opposed rather than series aiding. The output of the current amplifier appearing at point 37 is connected through coupling capacitors to the input grid of the voltage amplifier at point 41. Each amplifier is thus connected in feedback relation to the other as in Fig. 4 Both tubes V1 and V3 are of the remote cutofftype to provide a convenient means for varying the gain constants (i.e. turns-ratio) in response to a variable bias control voltage.L The transconductance of V4 is maintained sub stantially constant by operating the stage in a conventional maner with fixed bias. Variation of the turns-ratio is ef fected by jointly varying the gain constants K1 and K3 lby means of the bias voltages eel and pc2, respectively. vThe circuit is designed so that the current and voltage gains.

are maintained equal for a reasonably wide lrange of N, the equivalent control functions Ke versus eel and K1 versus ecz are made to track and by proper adjustment of the two potentiometers 61, 62, the biases ecl and ec'z can be derived from the single control voltage source 60,

The conventional xed turns-ratio transformer 63 shown connected to the input of the device is a useful adjunct to the circuit in that it permits grounded operation of both primary and secondary circuits, as shown.

Fig. 6 represents a telephone-type repeated amplifier 71 feeding a long section of transmission line '72 (for example, a section of undersea cable). To optimize the power transmitted to the receiving end of the line, and to minimize objectionable reflections of energy due to impedance miscatches, it is desirable to have the impedance looking into the cable (i.e. essentiaily the characteristic impedance of the cable, Z0, if it is a long section) matched in magnitude to the internal impedance, Ri, of the signal source (or repeater amplifier). This match usually is effected by a transformer having a turns-ratio equal to N where, recalling Equation 2a:

Often, however, because of variations in environmental conditions (such as temperature changes caused by ocean currents) the impedance looking into the sending end of the cable may vary continuously with time. (The impedance of the source usually is constant and usually is resistive. In general Z0 also is predominantly resistive.) lf a proper impedance match, i.e. R1=N2|Z0l, is to be maintained at all times, the lturns-ratio of the transformer should be varied so that N2jZ0l is always constant and.

equal to Ri. Continuous variation of the turns-ratio can only be approximated with conventional, close-coupled, tapped transformers. With the electronic transformer of the invention, however, such continuous variation of N is possible.

The circuit of Fig.6 is an illustration of how such an impedance match may be maintained constantly and automatically. ".[her long transmission line 7 Z with characteristic impedance Z is to be fed from the source 71 with constant resistive internal impedance, Ri. The variable transformer is used to match Z0 to Ri. To do this, an impedance bridge continuously makes a measurement of the impedance IZXI, namely the parallel combination,

of the source 71 and the load as seen through the transformer. The measurement is made at a frequency not used for communication, for example, in a guard band between two speech channels in a carrier transmission system. The impedance bridge is arranged to be balanced when ZX is equal to R1/2. When unbalanced, a smoothed error signal e proportional to (IZIl--Ri/Z) is 'developed by the detector 73. This control voltage may be additively combined witha manually set voltage EN (set originally to give the proper match) and the sum, ec, is usedy to determine the turns-ratio of the transformer. This control loop acts to maintain the proper impedance match when Z0 varies by automatically adjusting the turns-ratio N.

The control circuit functions in the following manner. Suppose EN is set to give the right value of N when the line is first connected, but, for some reason, Z0 is later caused to increase appreciably. Then, recalling Equation 35, N2|Z0j Ri and mismatch occurs. Simultaneously, however, the parallel combination of NZIZOI and R1 also increases so:

The resulting increased correction voltage (E+EN) reduces the turns-ratio, N, of the transformer until and NzjZolffeRi. (The precisenessV with which the adjustment is made is dependent upon thegain around the control loop.)

The invention has been described above as a substitute for a simple variable coupling transformer and as applied to match impedances in a transmission system. Many other applications of these principles may be found which fall within the scope of the invention, the particular embodiments described above being ones in which the invention performs a function peculiar to its nature and produces results previously nnobtainable except through the use of more complex and otherwise less satisfactory apparatus.

What is claimed is:

l l. An impedance transformer comprising a voltage amplifier having two input terminals and two output terminals, a current amplifier having two input terminals and two output terminals, the input terminals of said current amplifier being connected in series relationship to the output terminals of said voltage amplifier, and the input terminals of said voltage amplifier being connected in parallel with the output terminals of said current amplifier.

2. A transformer as defined in claim l wherein said voltage amplifier comprises an electron tube amplifier, and wherein said current amplifier comprises an electron tube amplifier.

3. A transformer as defined in claim 2 wherein said voltage amplifier comprises a variable mu tube input stage and an output stage in cathode follower connection connected in tandem therewith, and wherein said current amplifier comprises a variable mu tube input stage and an output pentode stage connected in tandem amplifier relationship with said secondnarned variable mu tube.

fi. A transformer in accordance with claim 3 wherein said variable mu tubes are resistively connected to a voltage source arranged to alter the current and voltage amplification ratios equally and synchronously.

5. An impedance transformer comprising a voltage amplifier having an input and an output, and a current amplifier having an input and an output, said voltage amplifier input being connected in parallel with said current amplifier output, and said current amplifier input being connected in series with said voltage amplifier output.

' 6. An artificial transformer comprising a current amplifier having an input and output, and a voltage amplifier having an input and an output, said amplifiers having 'equal gain factors and the input of each amplifier being connected with the output of the other whereby each amplifier is in feedback relation to the other.

7. An articial transformer comprising a voltage amplifier having an input and an output, a current amplifier having an input and an output, said amplifiers having the same amplification ratio, said voltage amplifierfinput being connected in parallel with said current amplifier output, and said current amplifier input being connected in series with said voltage amplifier, output.

8. In combination, apparatus in accordance with claim 7 and unicontrol means to adjust said amplification ratio whereby the effective turns-ratio of said artificial transformer is varied.

9. Apparatus in accordance with claim l, wherein said current amplifier and vsaid voltage amplifier comprise electron tube amplifiers of the Variable mu type, said tubes being connected to adjustable sources of bias voltage, whereby the amplification ratios of said current amplifier and said voltage amplifier may be equalized.

l0. Apparatus in `accordance with claim 9 wherein said sources of bias voltage are simultaneously variable thereby changing the effective turns-ratio of said transformer.

ll. The apparatus in accordance with claim l0 wherein said biassources comprise a pair of potentiometer resistors connected in parallel across a common source O Variable voltage, one resistor being tapped to supply 9 bias for said voltage amplifier, the other resistor being tapped to supply bias for said current amplifier.

12. In combination, a source of electrical communication signals; a transmission line terminated at its distal end by substantially its characteristic impedance; a variable artificial transformer having input terminals, output terminals, and control terminals connected between said source and the proximal end of said transmission line to match the impedance of said source to that of said line; an impedance bridge connected at the common terminals of said source and said transformer to measure the apparent parallel impedance at said common terminals; and a detector converting the error signal of said bridge to a control signal connected to a control terminal of said transformer whereby the apparent turns-ratio of said transformer is adjusted to maintain a proper termination of said proximal end.

13. In combination, an artificial transformer having input terminals, output terminals, and control terminals, comprising a current amplifier and a voltage amplifier, the input of said current amplifier and the output of said voltage amplifier being in series with said input terminals, the output of said current amplifier and the input of said voltage amplifier being in parallel with said output terminals, and said control terminals being connected to control elements of said amplifiers to alter the current and voltage amplification ratios equally and synchronously; a source of electrical communication signals connected to the input of said transformer; a transmission line terminated at its distal end by substantially its characteristic impedance and at its proximal end connected to the output terminals of said transformer; an impedance bridge connected at the junction of said source and said transformer to measure the apparent parallel impedance at said juncture; and a detector converting the unbalanced signal of said bridge to a control signal connected to said control terminals whereby the apparent turns-ratio of said transformer is adjusted to maintain a proper termination of said proximal end.

14. A transformer as described in claim 2 wherein said voltage amplifier comprises a variable mu pentode electron tube and a triode tube connected in tandem therewith in cathode follower connection, and wherein said current amplifier comprises a Variable mu pentode tube the control grid of which is connected to said input terminals, and an output pentode tube connected in tandem amplifier relationship with said second named variable mu pentode tube, the anode of said output tube being connected to said output terminals.

l5. A transformer in accordance with claim 14 wherein said variable mu pentodes are resistively connected to a bias voltage source arranged to alter the respective current and voltage ampliiication ratios equally and synchronously.

Roberts May 27, 1941 Barney July 27, 1954 

